Internal problem ID [1389]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.6 THE METHOD OF FROBENIUS
II. Exercises 7.6. Page 374
Problem number: 37.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 51
Order:=6; dsolve(9*x^2*diff(y(x),x$2)-3*x*(7-2*x^2)*diff(y(x),x)+(25+2*x^2)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = x^{\frac {5}{3}} \left (\left (\ln \relax (x ) c_{2}+c_{1}\right ) \left (1-\frac {1}{3} x^{2}+\frac {1}{18} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+\left (\frac {1}{6} x^{2}-\frac {1}{24} x^{4}+\mathrm {O}\left (x^{6}\right )\right ) c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 77
AsymptoticDSolveValue[9*x^2*y''[x]-3*x*(7-2*x^2)*y'[x]+(25+2*x^2)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^4}{18}-\frac {x^2}{3}+1\right ) x^{5/3}+c_2 \left (\left (\frac {x^2}{6}-\frac {x^4}{24}\right ) x^{5/3}+\left (\frac {x^4}{18}-\frac {x^2}{3}+1\right ) x^{5/3} \log (x)\right ) \]